Question

If the mean deviation of the numbers 1, 1 + d, 1 + 2d, .... 1 + 100d from their mean is 255, then d is equal to :

• A. 20.0
• B. 10.1
• C. 20.2
• D. 10.0

Answer 1

Answer: (B)

Mean = $\frac{101+d(1+2+3+....+100)}{101}$
$=1+\frac{d\times 100\times 101}{101\times 2}=1+50d$
$\because$ Mean deviation from the mean = 255
$\Rightarrow \frac{1}{101}[\left|1-\left(1+50d\right)\right|+\left|\left(1+d\right)-\left(1+50d\right)\right|$
$+\left|\left(1+2d\right)-\left(1+50d\right)\right|+...+\left|\left(1+100d\right)-\left(1+50d\right)\right|]=255$
$\Rightarrow 2d\left[1+2+3+....+50\right]=101\times 255$
$\Rightarrow 2d\times \frac{50\times 51}{2}=101\times 255$
$\Rightarrow d=\frac{101\times 255}{50\times 51}=10.1$